American Mineralogist, Volume 71, pages 127-135, 1986

Local states of Fe2+ and Mg2+ in magnesium-rich olivines

JeN SreNer,t S. S. HArxrn, rNo J. A. Sewrcxrr'2

Dep ortment of GeosciencesUniversity of Marburg

3550 Marburg, Federal Republic of Germany

Abstract

s?Fe M0ssbauer spectra of a synthetic forsterite and of one natural olivine were studiedat temperatures between 4.2 and 1223 K. Spectra were also taken at pressures between Iand 30 kbar at 568 K and in external magnetic fields between 4 and 7 T at295 Kand 4.2K. The signs of the electric field gradient at Ml and M2 arc positive. The average valueof the two asymmetry parameters a is 0.20+0.05. The force constants of Fe2+ at Ml andM2 are 4.7 +0.1 eY/42 and 4.2+O.l eY/A', respectively. The axial splitting d is I 120+50cm-' for both sites. The comparison of the 57Fe data with the previous 'z5Mg data allowsa more detailed analysis of total, lattice, and Fe2* valence field gradients at the Ml andM2 sites. The observed apparent lack of site preference for Fe2+ can be interpreted in termsof the local electronic properties.

Introduction

Many physical properties of olivines (Fe,Mg)rSiOo aredetermined by the local states of bonding at the atomicpositions and their dependences on temperature and pres-sure. The crystal structures of olivines are orthorhombicwith space group Pnma. In this paper we are particularlyconcerned with the local properties ofthe positions ofthebivalent cations, Fe2* and Mg2+, which are octahedrallycoordinated. There are two distinct positions, M I and M2,with point symmetries 7 and m, respectively. The distri-bution of the Fe2* and Mg2+ ions is generally disorderedover Ml and M2, although possible preferences of Fe2+for Ml or M2 under certain conditions have been debatedin the past. Many questions, particularly the cationic ex-change between Ml and M2 at elevated temperatures andits kinetics are still open. However, for the interpretationofsuch processes, detailed studies ofthe local site prop-erties are desirable.

In the past, Mdssbauer spectroscopy of 57Fe has beenmainly used for studying iron rich olivines (Eibschiitz andGaniel, 1967; Kiindig etal.,1967; Bush et al., 1970). Inthe present work we describe Mdssbauer studies of syn-thetic and natural olivines with low concentrations ofiron(0.0025 and 0.1 mol. fraction). The experiments were car-ried out in a wide range of temperatures (4.2-1223 K), athigh external fields (4-7 T), and at high pressure (30 kbar)and elevated temperature (568 K).

In this paper, the measured magnitudes, signs, andasymmetries of the electric field gradient (EFG) tensorsof 5?Fe in forsterite are compared with the 2sMg nuclear

I On leave from Institute of Physics, Jagiellonian University,30-059 Cracow. Poland.

2 Present address: Chalk River Nuclear Laboratories, ChalkRiver, Ontario, Canada.0003{04v8 6 / 0 to24 | 27 502.00

magnetic resonance data previously obtained for the samemineral (Derighetti et al., 1978) and with theoretical EFGcalculations. Such comparison is interesting in view of therelationship between lattice and valence contributions tothe total EFG. This may be a step towards a more generalconsideration of local structure and chemical bonding. Inparticular, the estimated axial field splittings of the iron3d orbitals can tentatively explain the weak, ifany, pref-erential site occupancy by Fe'z+ ions, which appears to beindependent of the external state during the crystallizationof olivine.

The Mossbauer spectra, if measured over a wide tem-perature range, also supply information about the dynam-ics of Fe2* ions. For this, the estimated Debye tempera-tures and force constants for both sites may be comparedwith X-ray diffraction studies at high temperatures andhigh pressures provided that sufrciently refined data areavailable.

Samples

Two maenesium-rich olivines with the following compositionswere studied. Sample (1): (Feo.-M&eers)rsiOo. This forsteritesample was obtained by powdering a single crystal specimen ofhigh perfection grown using the Czochralski method. High en-richment of 57Fe (90.470) permitted the recording of Miissbauerspectra with a high total resonant absorption effect of I 80/o despitethe low concentration of iron. Sample (2): (FeootMgo r)rSiOn. Thissample was kindly provided by T. Malysheva. It was a hightemperature olivine separated from a natural garnet peridotite.

The absorbers for the measurements at 295, 78 and 4.2 K weremade by mixing powdered samples with lucite powder. Pelletswith a diameter of 12 mm were prepared by heating at 420 Kand pressing at 2 kbar for 30 minutes. For high temperaturemeasurements the samples were mixed with boron nitride anddistributed homogeneously on an iron-free beryllium plate, alsol2 rnm in diameter. The absorber thickness was about 0.1 mg

r27

128 STANEK ET AL.: LOCAL STATES OF Fd* AND Mg,* IN OLIVINES

---------------szo

GGo

o

z

2

UE

Fig. I . Design of the high pressure, high temperature cell. ( I )sample, (2) graphite heater, (3) cupper connection, (4) pyrophilitefiller, (5) BnC anvils, (6) stainless steel rings, (7) thermocouple inAl2O3 tube fixed in a steel screw.

sTFe/cm2 for sample (l) and about 4 mgFe/cm2 for sample (2)so that the samples could be approximately treated as "thin"absorbers.

Measurements

The Mtissbauer spectra in the temperature range between 295and 1223 K were recorded using a vertically operating, watercooled furnace with a tungsten filament. The vacuum during themeasurements varied from 5 x l0-5 to l0-3 Torr, depending onthe temperature which was stabilized within 2 I(

Measurements in high, external magnetic fields were carriedout using a superconducting solenoid which allowed the takingof spectra at liquid helium, liquid nitrogen, and room tempera-tures. The direction of the gamma rays was parallel to the mag-netic field. The source was kept at a "zero field" position 4 cmfrom the absorber. This fortunate source-to-absorber geometrywas possible due to a field compensation coil in the solenoid atthe side of the source. However, the experimental line width inthe absorber was generally broadened to widths of about 0.28mm/s probably due to tlle fact that the magretic field at thesource was not exactly zero.

The apparatus used for the measurements ofM0ssbauer spectraat high pressures was the equipment described by Amthauer etal. (1979) modified for high temperature work up to 600 I( Thistemperature is needed for obtaining the resolution ofthe distinctquadrupole splittings of 57Fe at Ml and M2. The investigatedsample was mixed with BN powder, inserted into a graphite ring(4 mm in diameter), and pressed between two B4C anvils. Thecurrent through the graphite ring, being the main heating element,was 40 A at 500 K. The temperature of the sample was measuredby a Pt-Pt (10o/o Rh) thermocouple, which was used also fortemperature regulation (+2 K). The correction for the pressure-induced change of the thermoelectrical voltage given by thethermocouple was considered (Bundy and Strong, 1962). Thepressure vs. applied force calibration was carried out at roomtemperature using the known resistivity jumps of bismuth at 25.4and27 kbar (Bundy and Strorg, 1962) and ofytterbium at 40kbar (Drickamer, 1965). The constant force during experimentswas supplied by an automatically regulated hydrostatic press.Thus, there was no change in pressure during heating from 300to 500 IC

The design ofthe high pressure, high temperature cell whichhas not been published before is shown in Figulg | . lligh pressure,

-L -2 u..oi,r , rr .r1r

t '

Fig. 2. Miissbauer spectra of sTFe in polycrystalline forsteriteat temperatures as marked. The solid lines are Lorentzian linefits with widths and intensities constrained to be equal for thelow and high velocity peaks of each doublet.

high temperature Mtissbauer spectroscopy measurements havebeen attempted using a diamond cell heated with a laser beam(Ming and Bassett, 1974). The advantage ofour design is that ityields undistorted spectra based on thin absorbers with reason-ably large areas. However, the range of temperatures at presentis limited to about 700 K due to the thermal properties ofstainlesssteel (Thyrodur 2709) gasket.

All experiments were performed using a singleJine source ofs'Co in metallic Pd or Rh matrices. The activity of the sourcevaried from 20 to 40 mCi in the diferent experiments. Theinstrumental line width was smaller than 0.25 mm,rs. The velocityscale in the Mdssbauer spectra was calibrated by use of a metalliciron absorber.

Experimental results

Measurements at high temperatures

The temperature dependence of the Miissbauer spectrain forsterite doped with 5?Fe (sample l) was investigatedbetween 295 K and 1223 K. Spectra taken at 295, lO23and 1223 K are shown in Figure 2. High temperaturemeasurements were also carried out for the natural olivine(Feo,Mgr)rSiOo (sample 2).

STANEK ET AL.: LOCAL STATES OF Fd* AND ME* IN OLIVINES r29

9.0,,E

5UE

TEsao

T (K }Fig. 3. Temperature dependence ofthe total area under the

57Fe spectra of synthetic forsterite (sample l; O) and natural ol-ivine (Feo, Mg.r)rSiOn, (sampl e 2; ). 0

" : 37 4 + 5 K for forsterite

and dD: 375+5 K for natural olivine.

Since the two quadrupole-split Fe2+ doublets at the Mland M2 positions of olivine strongly overlap, the fittingprocedure is generally difrcult. In our case, however, be-cause ofhigh crystal perfection and absence ofany texturaleffects physically reasonable constraints can be assumedfor the fit. Consequently, the spectra were fitted in threediferent ways with the constraints

3oo soo TtKi

Fig. 5. Temperature dependence of the QS of 57Fe at Ml (solidpoints) and M2 (open points) in natural olivine (Feo,Mgor)rSiOo(sample 2).

wl: wfr, wi: wa,Ii_: I[, r?:rh; (a)W|: Wfr: Wi: W?.,Ii.:I l ' ,17:1tr' &)

wi. : wfr : wi : wa,I i : I f r : I7: Ih. (c)Here W and I are the line widths and intensities, thesuperscripts I and 2 refer to the M I and M2 sites, and Land H are the low and high energy lines, respectively, ofthe doublets. The final values for the quadrupole splittingQS, isomer shift IS and area A are the averaged resultsobtained from these fits. The errors given include thedifferences between the different schemes of fitting. Thedata on the temperature dependencies ofthe total areas

?EEoo0.7

E

FL

Io

tul

o@

T ( K }

Fig. 4. Temperature dependence of the 57Fe thermal shifts insynthetic forsterite (sample 1). The solid lines represent leastsquares fits based on equation (2), yielding force constants Kl :4.7 eV/4, (Ml, solid points), K2: 4.2 eV/4, (M2, open points).The solid and open squares show the temperature dependenceof the thermal shifts for (Feo,Mgor)rSiOo (sarnple 2) (they werenot included in the fit).

tO00 T t Kl

Fig. 6. Temperature dependence ofthe QS of 57Fe at M I (solidpoints) and at M2 (open points) in synthetic forsterite (samplel). The solid lines are the least squares fits based on equation (3)and equation (7) yielding 6 : I 120 + 50 cm-' for both positions.The dashed line is the calculated temperature dependence ofQSfor d : 1860 cm-' reported by Burns, 1970. The QS values at4.2 K and at 78 K were not included into the fit.

o

o

a Oo

oa

a o

aa

130 STANEK ET AL.: LOCAL STATES OF FE* AND Mg,, IN OLIVINES

tzoFLE

Id)

FzzaU

where .ER is the recoil energy of the nucleus (1.95 x l0-3eV for 57Fe), { is the recoil free fraction ofthe absorber,andCisaconstant .

Thp least squares fit ofequation (l) to our data is shownin Figure 3. The fit yielded 0D:374+5 K for syntheticforsterite (sample l) as well as for natural olivine (sample2). In our case, the ratio of A at Ml and M2 turned outto be independent of f within a fitting error of 20lo so that0o may be assumed to be the same for iron at both sites.This assumption is in agreement with earlier results (Bush

et al., 1970) obtained for fayalite, an iron-rich olivine, anda magnesium-rich olivine. In that work it was also con-cluded that the recoil free fraction ofiron at the Ml andM2 positions was the same within 2ol0.

The high temperature Mdssbauer spectra also suppliedvalues for the force constants of the Fe2* ions at the Mland M2 positions. In the higher temperature limit thethermal shift, i.e., the temperature dependence of the shiftof the Mdssbauer spectrum may be approximated (Guptaand Lal, 1972)by

dIS 3h2 ,,dl.JJ-f,i:_ffi*,"# (2)

Here, E" is the energy of the gamma transition (14.4 keV),M is the mass of 5?Fe, M : 9.465 x l0-" kg, and K isthe force constant. Substituting f obtained from the tem-perature dependence ofthe resonant area and fitting theexperimental IS for each doublet, K(Ml) : 4.7 +0.1 eY/;i 11.45 x loa dyn/cm'z) and K(M2):4.2+0.1 eY/42(6.66 x lOa dyn/cm'z) are obtained. The fits together withthe experimental IS values are shown in Figure 4.

Measurements of forsterite in high,external magnetic ftelds

The main pulpose of measuring Mdssbauer spectra inhigh, external magnetic fields H was the determination ofthe sign of the principal component V'' of the EFG tensor3at the Ml and M2 positions. Such spectra also allow usto estimate the asymmetry parameter 4; ? : (Vxx - Y"")/Vo, where V**, Vr" andYrtare the values of the secondderivative of the electrostatic potential V at the crystal-lographic positions of 5?Fe, and X,Y ,Z refer to the diago-nalized system.

The sign ofV,and value ofrl were foundby comparisonof the experimental spectra with those computed by meansof the "Gabriel-Ruby" program for calculating combinedquadrupole and magnetic hyperfine interactions in poly-crystalline samples (Gabriel, 1965; Collins and Travis,1967). The magnitudes of the quadrupole splittings ob-served in zero-field spectra and experimental line widthsof 0.28 mm/s were introduced as fixed parameters. Sincethe spectrum consists of two overlapping doublets due to

Fcf. Dir"*rioo.

-4 -2 u.roa9,r, ,..rr1

t'

Fig. 7. Mdssbauer spectra of forsterite at I bar (A) and 30kbar (B) at 568 K. The spectra were not corrected for the back-ground count rate produced by the iron impurities in the BoCanvils.

under the spectra are shown in Figure 3, the thermal shiftsare presented in Figure 4, and the temperature dependen-cies of the quadrupole splittings QS are plotted in Figures5 and 6.

The spectra of synthetic forsterite (sample l) taken attwo different pressures at 568 K are shown in Figure 7.An increase of l0o/o of the total area of absorption lineswas observed, but the spectra did not show any measur-able change in QS.

While the overlap of the Ml and M2 paramagneticdoublets in olivines is nearly complete between 4 and295K, a distinct separation of the doublets occurs at temper-atures higher than 500 K. QS plots from a larger numberof spectra at temperatures between 295 and 623 K (Fig.5) reveal that the temperature dependencies of the QS arealmost linear over that range. There is no discontinuityat any temperature. First, the areas of the doublets willbe analyzed in more detail. In the higher temperaturelimit, i.e., for T > 0.50o where do is the Debye tempera-ture, the decrease ofthe total area A under the absorptionspectrum of a thin absorber depending on temperaturecan be expressed as

A:ct:c'*n(-*ff) (1)

STANEK ET AL.: LOCAL STATES OF FdT AND ME, IN OLIVINES l 3 l

r00

:<

z

c

d}

z

z@UE

8z.

(L

X o na(D

z.zoaU Y Oe.

Fig. 8. Computed (solid line) and experimental (dots) 5?Fespectra in polycrystalline forsterite in external magnetic fields of4.0 T (A), and 6.0 T (B) at 295 K. The field was parallel to thegamma rays. For the computed spectra, n:0.2 and a positivesign of Vo were assumed.

Fe'?+ at the M I and M2 sites various simulations of spectrahad to be computed using positive and negative signs ofV' as well as diferent 4 values for both sites and differentexternal magnetic fields. a was varied between 0 and I insteps of 0.05. The simulations showed that the spectrumdepends on 4 and the sign of V,' most critically at fieldsbetween 4 and 7 T. The best agreement between experi-mental and computed spectra was obtained for a positivesign of Yu at the Ml as well as the M2 sites, and anaverage 4 : 0.20+0.05. Two experimental and computedspectra for fields H : 4.0 T and 6.0 T are shown in Fig-ure 8.

The application of the Gabriel-Collins procedure usedfor the evaluation of Mdssbauer spectra needs furthercomment. It is only correct for diamagnetic ions, or forparamagnetic ions which have isotropic properties as, forexample Fe3+. Fe2+ in forsterite is, however, anisotropic,i.e., the effective magnetic field at 57Fe, H"n, is not parallelto the external field H. Its magnitude depends on theorientation of the crystal with respect to the external field.In this case a phenomenological model which describesthe Mdssbauer spectrum of paramagnetic powders in high

6

YELOCITY (mm/s)

Fig. 9. 57Fe spectrum in polycrystalline forsterite at 4.2 K inan external magnetic field of 7.15 T parallel to the transmittedgamma rays.

magnetic fields developed by Varret (1976) may be ap-plied. It is based on the assumption that H"o acting at theFe2+ nucleus can be described as

H"r: (l + E)H

where E is the "magnetization hyperfine tensor." Suchmagnetization effects become significant at low temper-ature and at the high field limit, when saturation of themagnetization in the easy direction appears. This candrastically change the line shape of the M6ssbauer ab-sorption. Such an approach has been successfully used forthe description of 57Fe spectra of Fe andZn fluorosilicatesstudied in external fields (Varret,1976).

For a verification of the data obtained, an additionalexperiment at H : 7.l5 T and 4.2 K was made. The spec-trum obtained, shown in Figure 9, consists of two broadlines and can not be reproduced by the simple methodused in this paper due to enhanced magnetic anisotropyofFe2+ at lower temperatures as discussed above. In con-sequence, this result supplied no independent estimate forthe 4 value (the sign is obvious from room temperaturespectra).

It is to be noted that the sign of the V,, component ofthe EFG tensor as well as the asymmetry parameter forFe2+ in forsterite are the same at both sites as in fayalite,FerSiOo. The components of EFG tensor in fayalite N u >0 and a :0.2 at Ml and M2 sites) were estimated byKiindig et al. (1967) on the basis of the Mdssbauer spectraof the magnetically ordered state at 4.2 K.

A drastic difference is observed, however, between theEFG measured at Fe2+ and at Mg2+ ions in forsterite. Thecomponents of EFG tensors at Mg2+ in forsterite havebeen precisely determined by Derighetti et al. (1978) by

- 6

(3)

132 STANEK ET AL.: LOCAL STATES OF Fd* AND ME* IN OLIVINES

means of magnetic resonance on dynamically polarized25Mg nuclei in a single crystal. The given values of theasymmetry parameters are larger: 0.4 atM2 and 0.96 atMl. The signs of the main EFG components were notdetermined experimentally but a calculation based on thepoint charge model including ionic, dipole and quadru-pole contributions as well as overlap effects lead to pos-itive signs (Rager and Schmidt, l98l). These results, to-gether with our data are the basis ofthe discussion oftherelationship between lattice and valence EFG, presentedin the next section.

Discussion

Correlation between lattice qnd valence fteld gradient

A prirnary interest ofthis study was the relation betweenthe EFG tensors of sTFe and 25Mg (Derighetti et al., 1978)at the two nonequivalent Ml and M2 sites. The 57Fe ten-sors are described in their principal axes system X,y,Zand consist of two contributions: (l) the dominating va-lence contribution V; with the principal axes systemX*,Y*,2* and(2) the lattice contribution Vl, with the prin-cipal axes system x,y,z. According to the model of Ingalls(1964) it is usually assumed that the systems X,Y,Z,X*,Y*,Z* and x,y,z have identical orientation. For the2sMg tensor, of course, Y; is assumed to be zero, i.e., V,, :

Vl,. A discussion of the sigrrs of the various tensors andthe ditrerent orientations of their principal axes appearsworthwhile.

For comparing the lattice tensors acting on 57Fe and'?sMg with the total tensors, the data should be correctedfor the different Fe2+ and Mg'z+ Sternheimer antishieldingfactors 7-. Thus at 57Fe the lattice tensor is

vl,(Fe,*): #rffi x v'(Ms,*) (4)

where'y-(Mg'z+; : -3.5 (Schmidt et al.,1979), ?-(Fe'z+; :-10.972 (Sternheimer,1972), and i: x,y,z. Assuming apositive sign of V-(Mg2+) (Rager and Schmidt, l98l) andsubstituting the experimental data for Vu(Mg'?*) (Deri-ghetti et al., 1978), yields the values for the 57Fe latticetensor components at both positions4 expressed in theprincipal axes system, x,y,z.

The estimation of the errors in Vl(Fe'*) is difficult. Theexperimental errors of Vl,(Mg2+) are about l0re V/m2. Theerrors of calculated 7-(Fe2+) and "y-(Mg'?*) are not known;they can even reach 100/0, but this causes only systematicshifts ofV|(Fe2+). In particular the value of the asymmetryparameter 4 is not affected.

However, the question of how much the lattice EFGmeasured on Mg2+ ions can be identified with the latticeEFG acting on Fe2+ at the same crystallographic position

a An energy shift of I mm,/s for the 14.4 keV transition in the57Fe Mdssbauer spectrum is equal to 11.625 MHz, or to 4.808 xl0-e eV. An axial tensor of Vo: 10" V/m'z produces a quad-rupole splitting of 57Fe of 0.208 mm/s (assuming Q : 0.20 xl0-20 cm2 for the quadrupole moment of 14.4 keV state of sTFe).

s00 1000 1s00

6 (cm-1 )

Fig. 10. The asymmetry parameter of a positive valence EFGcalculated for 295 K in the function ofthe axial field splitting 6.The ditrerent lines refer to different 6'ld ratios, as marked. Theexperimental points (i) and (ii) result from two possible relativeorientations ofthe valence and lattice EFG tensors.

is still open for discussion. The two gradients may differbecause of the different overlap contribution, which atleast in the Mg2+ case is meaningful (Rager and Schmidt,l 98 l ) .

For obtaining the valence EFG, V;, the lattice EFGtensor expressed in the x,y,z frame must be subtractedfrom the total EFG tensor. From a comparison of the dataof Kiindig et al. (1967) and Derighetti et al. (1978), it isfound that at the M2 position V,' is parallel to V! (theZ axis coincides with the y axis). For further discussionit is reasonable to assume that not only is Z parallel to ybut also (l) zllY and xllX, or, alternatively, (2) zllX, xllY.Using the proper transformation matrix, describing therotation by 90'around the x axis for case (l) and rotationby 90" around x and y axes for case (2) the Vl, tensor canbe transformed to the X,Y,Z frame, now being identicalto the X*,Y*,Z* axes system. By this procedure, Vii :

Vo - Vl (for i + j, V,,,Vl,,Vj : 0).The first transformation leads to a highly asymmetrical

valence EFG tensor for Fe2+ with a":0.33 and shouldbe excluded from further discussion, according to the fol-lowing considerations.

The asymmetry parameter of,the valence tensor, 4", ofthe Fe2+ ion in a distorted octahedrally coordinated siteis caused by the unequal population of rhe 3d*,,3d-and3d,, levels. If the ground state of Fe2+ is 3d*, the Yo ispositive. The a is determined by the temperature, by the

STANEK ET AL.: LOCAL STATES OF FE* AND ME* IN OLIVINES r33

Table l. The components of the lattice (l), total and valence(v) EFG tensors in Ml and M2 sites, expressed in the total EFG

tensor principal axis system X,Y,Z in the units of 1020 V/m,

1 --1 _l-qo( u$a uzz Vlo< Vy" Yzz vV vv ,rV')o( 'w 'zz

+2O -6-57 -85 +142-59 -88 +147

axial field splitting 6, and by the rhombic field splitting6, : l2D, where D is rhombic field parameter accordingto equation (5) (Ingalls, 1964)

Plxz) - P lyz)

t -Lrp6zl- Plyz))

(5)

where P I yx), P I xz), P I xy) are the populations ofthe 3d"",3dn and 3d-, orbitals.

?" was calculated as a function of D for T : 294 K andfor different D,/D ratios. The result is shown in Figure 10.Assuming a" : 0.33 (case (l)) leads to a 6 of less than 300cm-'. Such small axial field splitting would lead to a veryfast decrease of the quadrupole splitting with increasingtemperature. This is inconsistent with our data (see thefollowing section). In summary, we believe that case (2),i.e., xllY, yllZ, zllX, leadingto anearly axial valencetensor,must be chosen.

The discussion ofthe tensor at the Ml site is less straight-forward. First,4' :0.964, i.e., Vl, = -Vl-, and the as-signment of axes, as well as the discussion of the signbecome irrelevant. Second, because of the crystallographicpoint symmetry I at Ml, the systems X,y,Z, and x,y,zdo not coincide with any crystallographic axis. Moreover,the orientation of the total tensor obtained from Mdss-bauer measurements is subject to considerable error.

At any rate, according to Kiindig et al. (1967) and De-righetti et al. (1978), the angle between Z and,z or, alter-natively, Z and y, is about 15", i.e., the Z and z axes arenearly parallel. Ifthe second orientation is arbitrarily cho-sen, i.e., Z parallel to y, Vlj at the Ml site may be treatedas in the case of M2.

In Table I the components of the lattice (Vl), valence(V;) and total (V,,) tensors expressed intheX,Y,Z systemare presented. The Vl, components are calculated from thedata of Derighetti et al. (1978) using equation (4) andtransformed to the X,Y,Z system. The V' values wereobtained using the equation

where QS is the experimental quadrupole splitting, andn:0.2 is the experimental value of the asymmetry pa-rameter of the total tensor. Finally, VI : Vo - Vl,.

Considering the data collected in Table l, it can beconcluded that in spite ofthe fact that the lattice tensoris highly asymmetric (especially at Ml) the valance con-tribution to the total tensor is, at room temperature, fairlyaxial (a":0.018, as estimated from Table l) i.e., it isindicative ofa big axial field splitting.

The experimental results on forsterite appear to weakenthe prediction of Ingalls (1964) concerning the relationbetween the lattice and valence contributions to the totaltensor (they should be of opposite signs and the x,y,zsystem should be identical with the X,Y,Z system).

Temperature dependence of the quadrupole splitting(QS) and the axial fwld spliuing 6

The temperature dependence of the valence tensor ofFe2+ was described by Ingalls (1964). The ligand fieldparameters (cf. also Gibb, 1968) can be estimated fromthe decrease of the QS with the increasing temperature ifthe weakly temperature dependent lattice contribution issubtracted from the total tensor. In our present case, thelattice tensors in forsterite are, ofcourse, known preciselyat4.2Kfrom the 2sMgdata of Derighetti et al. (1978). Inolivines, two opposing contributions to the temperaturedependence ofthe lattice tensor may be expected: (l) ther-mal expansion of the lattice may reduce the tensor withincreasing temperature; (2) the increasing mean static dis-tortion of the oxygen octahedra around Ml and M2 withincreasing temperature (Smyth and Hazen, 1973; Smyth,1975) may produce an increasing contribution to the ten-sor. This contribution may partly cancel or even outweigh( l ) .

For further discussion the high temperature (568 K)and high pressure (30 kbar) M0ssbauer measurementsshould be included. It is known that the ratio of the coef-ficient of linear thermal expansion a, and the coefficientof linear compression B, are constant for a wide varietyof minerals (Hazen, 1976, 1977). Thus the process of thethermal volume decrease is structurally similar to the de-crease of volume during compression. For forsterite, apressure diference of 30 kbar corresponds to a decreaseof the average M-O bond of about 0.018 A. The samedecrease is achieved by a decrease in temperature ofabout700 K (Hazen 1976). No pressure dependence of the QSwas observed at 30 kbar (cf. Fig. 7). lt can, therefore, beconcluded that structural changes expected in our exper-imental temperature range (300-1220 K) have little in-fluence on the lattice tensor, which can be assumed to beindependent of temperature.

In the high temperature region, where the influence ofspin orbital interaction on the tensor is negligible, thetemperature dependence of an axially symmetric valencetensor V2, at an octahedrally coordinated site of Fe2+(Ingalls, 1964) is

Y2: -2Y:,": -2Vk: C x ,l ,--eipl;4u.4,? (7)l + 2 e x p ( - 6 / k t 1

-23ttlt42

-81 44 +165-79 -82 +161

J

? " : ;z

, *'[-(' -;') l14-.-{-(' .i',) /14

" -i{.4- F;,)I14...{-(, .;,)I14}

n2T ;

Jos: f"o (6)

134 STANEKET AL.: LOCAL STATES OF FE* AND ME, IN OLIVINES

Here d: 3D, is lhe Tr" orbital splitting, where D" is theaxial field parameter. The values of the total componentsV' can be calculated for any temperature as

V'(Z): VI(l") +'Vl, (8)

To obtain the explicit form ofthe temperature dependenceof QS the V,,(7) components must be inserted into equa-tion (6). The experimental values of QS are presented inFigure 6. The least squares fit ofthe function ofequation(6) to the points of Figure 6 with the conditions describedby equation (7) (solid lines in Fig. 6) leads to d : I I 20 + 50cm-'. This result is inconsistent with d : 1860 cm-'(dashed line in Fig. 6) ofBurns (1970). It should be noted,however, that the value of 1860 cm-' results, at least forthe Ml site, from a numerical error in subtracting theenergy of 8060 cm-' and,7200 cm-' of the two absorptionbands in the polarized absorption spectra ofolivine (Burns,1970). Our result can be related rather well to the ab-sorption minimum of ll24 cm-' in the infrared spectraof forsterite (Runciman et al., 1973).

Preferential site occupancy of bivalentiron in olivines

In view of the different point symmetries of the Ml andM2 positions and the somewhat different geometrical dis-tortions of the Ml and M2 coordination octahedra a pref-erence ofFe2* is expected for one ofthe two positions, atleast in general. The EFG tensors are distinct for the twopositions, particularly at temperatures higher than 250C.Moreover, the average M-O distance is somewhat shorterfor Ml (d : 2.095 A; ttran for M2 (d : 2.131A) (Wentand Raymond, 1973), yielding a slightly smaller volumefor the Ml octahedron.

The relative volumes of Ml and M2 octahedra are con-sistent with the result that the force constant K(Ml) isgreater than K(M2). This fact indicates that the Fe2* ionsat Ml are somewhat more tightly bonded to the oxygenions than alM2. This result does not support the conclu-sion of Hazen (197 6) that the compressibility of M I oc-tahedra is larger than that of M2. From our data for theforce constants we find

responsible for the preference of Fe2+ for the M2 position(Burns, 1970). The apparent lack of cation ordering in

olivines appears to be related to the equal 6 splittings of

Fe2+ at both M positions as concluded from present data.Therefore, precise determination of Fe2+ ordering over

Ml and M2 in the olivine solid solution by Mdssbauer

spectroscopy will require careful experimental study of

the relative Ml and M2 resonant absorption areas over

a large region of temperature.The weak preferential site occupancy in olivines has

also been explained by a dynamical Jahn-Teller effect(Welsch et al, 197 4). However, in that work an incorrect

order of /r, level splitting was assumed, i.e., from the

distortion of the M2 octahedron it was concluded that theground state is a doubly degenerated (3d-.,3d-) level. Thepositive signs of V2 show that the ground states must be

3d-, singlets for both positions. Thus, the values of sta-bilization energy of Welsch et al. (197 4) require reconsi-

deration.

Acknowledgments

We thank T. Malysheva, Vernadsky Institute of Chemistry,Academy of Sciences USSR, Moscow, for a natural sample ofolivine. One of us (J. Stanek) thanks the A. V. Humboldt Foun-dation for a fellowship. This work was supported by a Grant ofGerman Research Foundation (SFB- I 27).

References

Amthauer, Georg, Fenner, J., Hafner, S. S., Holzapfel, W. B.,and Keller, R. (1979) Effect ofpressure on resistivity and Mdss-bauer spectra of mixed valence compound in SnrSr. Journalof Chemical Physics, 7 O, 4837 -4842.

Bundy, F. P. and Strong, H. M. (1962) Behavior of metals athigh temperatures and presswes. Solid State Physics (Advancesin Research and Application), 13, 8l-146.

Burns, R. G. (1970) Mineralogical Application of Crystal FieldTheory. Cambridge at the University Press, 79-84.

Bush, W. R., Hafner, S. S., and Virgo, David (1970) Some or-dering ofiron and magnesium at the octahedrally coordinatedsites in a magnesium rich olivine. Nature, 227 , 1339-1341.

Collins, R. L. and Travis, J. C. (1967\ The electric fietd gradienttensor. In I. J. Tensor, Ed., Mdssbauer Effect Methodology, 3,p. 123-161. Plenum, New York.

Derighetti, Bruno, Hafner, S. S., Marxer, H., and Rager, Helmut(1978) NMR of '?eSi and 2'Mg in MgrSiOn with dynamicalpolarisation technique. Physics ktters, 661', I5C-l52.

Drickamer, H. G. (1965) The etrect of high pressure on the elec-tronic structure of solids. Solid State Physics (Advances inResearch and Application), 17, l-134.

Eibschiitz, Marcu and Ganiel, U. (1967) M<issbauer studies ofFe2+ in paramagnetic fayalite. Solid State Communications, 5,267-270.

Gabriel, J. R. (1965) Computation of Mtissbauer spectra. In I.J. Gruverman, Ed., Mtissbauer Effect Methodology, l, p. l2l-132. Plenum. New York.

Gibb, T. C. (1968) Estimation of ligand-field parameters fromMiissbauer spectra. Journal of Chemical Society (A), 1439-1444.

Gupta, G. P. and Lal, K. C. (1972) Temperature shift, recoil-freefraction, and force constant in Miissbauer studies. Physica Sta-tus Solidi, 51, 233-239.

Hazen, R. M. (1976) Efect of temperature and pressure on thecrystal structure of forsterite. American Mineralogist, 60, 1280-1293.

Hazen, R. M. (1977) Effects of temperature and pressure on the

dv(M2)

In spite of the geometrical difference between the Ml andM2 octahedra the electronic levels of Fe2+ appear to bequite similar at both sites. This rather surprising result isconfirmed by the spectra at high pressures. The hyperfineparameters are not influenced significantly by pressuresup to about 30 kbar.

The ordering of cations may be discussed in terms ofthe crystal freld stabilization energy CSFE. For octahedralcoordination,

CSFE: ja. + jo (9)

where Ao is the crystal field splitting and 6 is the axial fieldsplitting (Burns, 1970). In pyroxenes, it was concludedthat the diference in D at the Ml and M2 positions is

0pdv(Ml) /r(vrrlY' ,o :\ff i7 ='o

STANEK ET AL.: LOCAL STATES OF FdT AND Mgh IN OLIVINES 1 3 5

crystal structure of ferromagnesian olivine. American Miner-afogist,62, 286J95.

Ingalls, Robert (1964) Electric-field gradient tensor in ferrouscompounds. Physical Review (A), 133, 787-795.

Kiindig, Walter, Cape, J. A., Lindquist, R. H., and Contrabaris,G. (1967) Some magnetic properties of FerSiOo from 4 K to300 K. Journal ofApplied Physics, 38,947-948.

Ming, Li-chung and Bassett, W. A. (1974) Laser heating in thediamond anvil press up to 2000qC sustained and 3000"C pulsedat pressure up to 260 kilobars. Review of Scientific Instru-m e n t s , 4 5 , l 1 l 5 - 1 1 1 8 .

Rager, Helmut and Schmidt, P. C. (1981) Electric field gradientcalculation in forsterite, MgrSiOo. Physics and Chemistry ofMinerals, 7, 169-176.

Runciman, W. A., Sengupta, Dipankav, andGourley, J. T. (1973)The polarized spectra of iron in silicates. II Olivine. AmericanMineralogist, 58, 45 1-456.

Schmidt, P. C., Weiss, Alarich, and Das, T. P. (1979) Effect ofcrystal field and self-consistency on dipole and quadrupolepolarizabilities of closed-shell ions. Physical Review (B), 19,552s-5534.

Smyth, J. R. and Hazen, R. H. (1973) The crystal structures offorsterite and hornolite at several temperatures up to 900'C.American Mineralogist, 58, 588-593.

Smyth, J. R. (1975) High temperature crystal chemistry of fayal-ite. American Mineralogist, 60, 1092-1097.

Sternheimer, R. M. (1972) Quadrupole shielding and antishield-ing factors for several atomic ground states. Physical Review(A),6, 1702-1707.

Varret, F. (1976) Miissbauer spectra of paramagnetic powdersunder applied field: Fe2* in fluorosilicates. Journal of Physicsand Chemistry of Solids, 37 , 265-27 l.

Welsch, D., Donnay, Gabrielle, and Donnay, J. D. H' (1974)Jahn-Teller effects in ferro magnesian minerals: pyroxene andolivines. Bulletin de la Soci6t6 Francaise de Min6ralogie et deCristallographie, 97, I 7f l 83.

Wenk, H. R. and Raymond, K. N. (1973) Four new structurerefinements of olivine. Zeitschrift fiir Kristallographie, 137,86-l 05.

Manuscipt received, December 3, 1984;acceptedfor publication, September 4, 1985.